1. Resolver la siguiente ecuación diferencial por el método de variación de parámetros :y´´ + y = sec ^ 2x?

Resolvemos la EDO homogénea

<img src="https://tex.z-dn.net/?f=y%27%27%2By%3D0%5C%5C%20%5C%5C%0Ar%5E2%2B1%3D0%5Cto%20r%3D%5Cpm%20i%5C%5C%20%5C%5C%0A%5Cboxed%7By_h%3DC_1%5Ccos%20x%2BC_2%5Csin%20x%7D" />

Luego con ayuda del Wronskiano tenemos :

<img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A%5Ccos%20x%20%26%20%5Csin%20x%5C%5C%0A-%5Ccos%20x%20%26%20%5Ccos%20x%0A%5Cend%7Bmatrix%7D%0A%5Cright%5D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0Au%27%5C%5C%0Av%27%0A%5Cend%7Bmatrix%7D%0A%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A0%5C%5C%0A%5Csec%5E2%20x%0A%5Cend%7Bmatrix%7D%0A%5Cright%5D%5C%5C%20%5C%5C%0A%5Cdisplaystyle%0Au%27%28x%29%3D-%5Csin%20x%20%5Csec%5E2%20x%5Cto%20u%28x%29%3D%5Cint%20%5Cdfrac%7B-%5Csin%20x%7D%7B%5Ccos%5E2%20x%7Ddx%5C%5C%20%5C%5C%0Au%28x%29%3D-%5Csec%20x%5C%5C%20%5C%5C%0Av%27%28x%29%3D%5Csec%20x%5Cto%20v%28x%29%3D%5Cint%20%5Csec%20x%5C%2C%20dx%5C%5C%20%5C%5C%0Av%28x%29%3D%5Cln%20%7C%5Csec%20x%2B%5Ctan%20x%7C%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7By%3D-1%2B%5Csin%20x%5C%2C%5Cln%20%7C%5Csec%20x%2B%5Ctan%20x%7C%2BC_1%5Ccos%20x%2BC_2%5Csin%20x%7D%7D" />.